关于${\mathbb R}^n$中无界凸集上容许${\mathbb C}^n$中全纯扩张的不可微可微函数空间及其对偶
On a Space of Infinitely Differentiable Functions on an Unbounded Convex Set in ${\mathbb R}^n$ Admitting Holomorphic Extension in ${\mathbb C}^n$ and its Dual
摘要：
考虑${\mathbb R}^n$中无界闭凸集上的无穷光滑函数空间。它表明，该空间中的每个功能可以扩展到整个功能在${\mathbb C}^n$满足某些规定的增长条件。得到了该空间上线性连续泛函的傅里叶-拉普拉斯变换刻画。本文还给出了回火分布的Paley-Wiener-Schwartz定理的一个变形。
英文摘要：
We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth condition. Description of linear continuous functionals on this space in terms of their Fourier-Laplace transform is obtained. Also a variant of the Paley-Wiener-Schwartz theorem for tempered distributions is given it the paper.
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